I am using Wordpress with the latest updates etc.  

I am hosting it with my own domain name and have recently changed the name of my business.  I want to transfer the plugins, blog postings, saved theme, everything over to the new name.  I am pretty familiar with msyql, wpconfig.php, and the Wp-admin panel.  What is the easiest way to make this transfer?  The web hosting is the same so I may even be able to use the same mysql database to save some time.  I've looked all over online and can't really find anything that talks about this.  Thanks in advance!  BTW.. this is all within Lunar Pages if that makes the answer easier.

simply moved your web folder to your required servers and edit config file .